Newton Raphson method (convergence problem)

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SUMMARY

The discussion focuses on the convergence issues encountered while implementing the Newton Raphson method in FORTRAN for calculating free energy. The user initially faced non-convergence in their results, which was attributed to insufficient iterations and potential errors in summation over an exponential series. Key modifications were suggested, including increasing the number of iterations and correcting the derivative expressions in the code. The user provided a revised version of their code, which incorporated these changes and aimed to achieve accurate calculations for the variable "cf".

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KarAnw
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Hello, I am new in the field of FORTRAN. I started to write a code using Newton Raphson method. Below is the code of main program portion only. During my calculation, I have found that my results are not converging, Any help or advice will be highly appreciated in this case.
Thank you for the effort of helping in advance. Program Free_energy
Implicit None
Integer:: i,j,l,k
Double Precision Gmic,U,Phi
Double Precision s,Uderv,cc,DG0,cf,ctot1,
& Keff,Cagg,ctot,sum,Cagg1,cnew,
& Cagg2,cctot1,kapp,error,Csalt,Csalt1,
& cext
Double precision :: Nelec
Double precision :: Nwat
Double precision :: Nlig

ctot = 1D0
cf=ctot/2
cext = 0.01

sum=0.0
DG0 = -100.0

Do While(DG0.le.20)

do i=0,2
do j=0,10
do l=0,10

Nelec=i
Nwat=j
Nlig=l

Keff=dexp(-Gmic(Nelec,Nwat,Nlig)-Nelec*DG0)
Cagg=Keff*((cf)**Nlig)
Cagg1=sum+Nlig*Cagg
Cagg2=sum+(Nlig**2)*Cagg

enddo
enddo
enddo

ctot1=ctot-Cagg1
cctot1=ctot-Cagg2

cnew = cf-(ctot1/cctot1)

error = abs((cnew-cf)/cnew)

cf = cnew

write(72,*) cf, error
if(error.lt.1D-7) exit

Csalt1 = 0.0

do i=0,2
do j=0,10
do l=0,10

Nelec=i
Nwat=j
Nlig=l

Keff = dexp(-Gmic(Nelec,Nwat,Nlig))
Csalt = Csalt1+Keff*((cf)**Nlig)*Nelec

enddo
enddo
enddo

Kapp = Csalt/cext

write(70,*) DG0, -log(kapp)/2
write(72,*) cf, -log(kapp)/2

DG0 = DG0 + 0.1

enddo
 
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I find that graphing the results of the iterations can be helpful.
 
Up the number of iterations and check for their convergence...it seems to me at first glance that you are not iterating enough.
 
First I would like to thank you both for the reply,

Since you have mentioned that increasing the iteration number may solve the problem, but my question is how can I do that?

Also in my code, the function has summation over an exponential series of the Gimc, I am afraid of that also because I think that summation is also not happening there properly.
Further, I made two changes in the expression of the derivative of my function (Cagg2) and the expression of Keff in my code. The rest of the code is unchangeable and almost like the previous one except that two lines. I ran this one and I find this plot (-log(Kapp)/2 vs DG0) attached with this reply. My aim was to calculate the "cf" which has also the negative values in the calculated results.

I would like to thank you again for the help. Any advice or direction in this case will become helpful to me in near future.

Note: For your interest, the new corrected version of the code (only the main program portion only) has been given below,

Program Free_Energy
Implicit None
Integer:: i,j,l,k
Double Precision Gmic,U,Phi
Double Precision s,Uderv,cc,DG0,cf,ctot1,
& Keff,Cagg,ctot,sum,Cagg1,cnew,
& Cagg2,cctot1,kapp,error,Csalt,Csalt1,
& cext
Double precision :: Nelec,kB,T
Double precision :: Nwat
Double precision :: Nlig

ctot = 1D0
cf=ctot/2
cext = 0.01

DG0 = -100.0
Do While(DG0.le.20)

do i=0,2
do j=0,10
do l=0,10

Nelec=i
Nwat=j
Nlig=l

Keff=dexp(-Gmic(Nelec,Nwat,Nlig)-Nelec*DG0)
Cagg=Keff*((cf)**Nlig)
Cagg1=sum+Nlig*Cagg
Cagg2=sum+(Nlig**2)*Keff*((cf)**(Nlig-1)) enddo
enddo
enddo

ctot1=ctot - Cagg1
cctot1=ctot - Cagg2
cnew = cf-(ctot1/cctot1)

error = abs((cnew-cf)/cnew)

cf = cnew

write(74,*) cf,error

if(error<1D-7)exit

Csalt1 = 0.0

do i=0,2
do j=0,10
do l=0,10

Nelec=i
Nwat=j
Nlig=l

Keff = dexp(-Gmic(Nelec,Nwat,Nlig))
Csalt = Csalt1+Keff*((cf)**Nlig)*Nelec

write(73,*) cf
enddo
enddo
enddo

Kapp = Csalt/cext

write(70,*) DG0, -log(Kapp)/2

write(72,*) cf, -log(Kapp)/2

DG0 = DG0 + 0.1

enddo
End
 

Attachments

  • app_free.png
    app_free.png
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part of your issue is that for example you define Nwat as a double, then assign an integer to it, yes it theoretically works, but better programming style is

Nwat = double(j)

it makes a double out of the j so that it is j.00000000
 
Thank you for the reply, I will follow your suggestion and let you know about the result.
 

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